The semantics is given in terms of interpretations
\(=(\Delta ^,\cdot ^)\) , we refer to
[1]} for details.
An interpretation satisfies a CI \(C \sqsubseteq D\)  if
\(C^\subseteq D^\) , a fact \(A(c)\)  if \(c \in A^\) , and a fact
\(r(c,c^{\prime })\)  if \((c,c^{\prime }) \in r^\) . We thus make the standard names
assumption, that is, we interpret constants as themselves. This
implies the unique name assumption. For \(S \subseteq \Delta ^\) , we
use \(|_S\)  to denote the restriction of to domain \(S\) .
An interpretation is a model of an ontology or database if it
satisfies all inclusions or facts in it. A database \(\)  is
satisfiable w.r.t. an ontology if there is a model of and .
